What shapes the optimal degree of progressivity of the tax and transfer system? On the one hand, a progressive tax system can counteract inequality in initial conditions and substitute for imperfect private insurance against idiosyncratic earnings risk. At the same time, progressivity reduces incentives to work and to invest in skills, and aggravates the externality associated with valued public expenditures. We develop a tractable equilibrium model that features all of these trade-offs. The analytical expressions we derive for social welfare deliver a transparent understanding of how preferences, technology, and market structure parameters influence the optimal degree of progressivity. A calibration for the U.S. economy indicates that endogenous skill investment, flexible labor supply, and the externality linked to valued government purchases play quantitatively similar roles in limiting desired progressivity.